A035521 Fifth column of triangle A035342; related to A035330.

0, 0, 0, 0, 1, 45, 1470, 43890, 1291815, 38710035, 1199167200, 38692476900, 1304976397725, 46070080281225, 1702810398539250, 65862570279255750, 2663551451057371875, 112503209942059311375, 4957166849516125744500

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

a(n) = A035342(n,5).

a(n), n>=5, enumerates unordered n-vertex forests composed of five plane (ordered) increasingly labeled ternary (3-ary) trees. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.

Examples

			a(6)=45 increasing ternary 5-forest with n=6 vertices: there are three such 5-forests (four one vertex trees together with any of the three different 2-vertex trees) each with binomial(6,2)= 15 increasing labelings. W. Lang, Sep 14 2007.
		

Crossrefs

Cf. A000108, A035342, A035330.

Formula

a(n) = n!*A035330(n-4)/(5!*2^(n-5)), n >= 5; E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^5)/5!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.